Question

bashir leans a 16 - foot ladder against a wall. if the ladder reaches 14.3 feet up the wall, what angle does it form with the ground? round your answer to the nearest tenth of a degree.
answer attempt 1 out of 2

Explanation:

Step1: Identify the trig - ratio

We have a right - triangle situation where the ladder is the hypotenuse ($c = 16$ feet) and the height on the wall is the opposite side ($a = 14.3$ feet) to the angle $\theta$ that the ladder makes with the ground. We use the sine function, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin\theta=\frac{14.3}{16}$

Step2: Calculate the sine value

$\sin\theta=\frac{14.3}{16}=0.89375$

Step3: Find the angle

To find $\theta$, we take the inverse sine (arcsine) of 0.89375. $\theta=\sin^{- 1}(0.89375)$
$\theta\approx63.3^{\circ}$

Answer:

$63.3^{\circ}$